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Register a new userCoupling of pion condensate, chiral condensate and Polyakov loop in an extended NJL model
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The Nambu Jona-Lasinio model with a Polyakov loop is extended to finite isospin chemical potential case, which is characterized by simultaneous coupling of pion condensate, chiral condensate and Polyakov loop. The pion condensate, chiral condensate and the Polyakov loop as functions of temperature and isospin chemical potential are investigated by minimizing the thermodynamic potential of the system. The resulting $(T,mu_I)$ phase diagram is studied with emphasis on the critical point and Polyakov loop dynamics. The tricritical point for the pion superfluidity phase transition is confirmed and the phase transition for isospin symmetry restoration in high isospin chemical potential region perfectly coincides with the crossover phase transition for Polyakov loop. These results are in agreement with the Lattice QCD data.
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The critical endpoint (CEP) and the phase structure are studied in the Polyakov-loop extended Nambu--Jona-Lasinio model in which the scalar type eight-quark (sigma^4) interaction and the vector type four-quark interaction are newly added. The sigma^4 interaction largely shifts the CEP toward higher temperature and lower chemical potential, while the vector type interaction does oppositely. At zero chemical potential, the sigma^4 interaction moves the pseudo-critical temperature of the chiral phase transition to the vicinity of that of the deconfinement phase transition.
The Polyakov loop extended Nambu--Jona-Lasinio (PNJL) model with imaginary chemical potential is studied. The model possesses the extended ${mathbb Z}_{3}$ symmetry that QCD does. Quantities invariant under the extended ${mathbb Z}_{3}$ symmetry, such as the partition function, the chiral condensate and the modified Polyakov loop, have the Roberge-Weiss (RW) periodicity. The phase diagram of confinement/deconfinement transition derived with the PNJL model is consistent with the RW prediction on it and the results of lattice QCD. The phase diagram of chiral transition is also presented by the PNJL model.
With the isovector coupling constants adjusted to reproduce the physical pion mass and lattice QCD results in baryon-free quark matter, we have carried out rigourous calculations for the pion condensate in the 3-flavor Nambu-Jona-Lasinio model, and studied the 3-dimensional QCD phase diagram. With the increasing isospin chemical potential $mu_I$, we have observed two nonzero solutions of the pion condensate at finite baryon chemical potentials $mu_B$, representing respectively the pion superfluid phase and the Sarma phase, and their appearance and disappearance correspond to a second-order (first-order) phase transition at higher (lower) temperatures $T$ and lower (higher) $mu_B$. Calculations by assuming equal constituent mass of $u$ and $d$ quarks would lead to large errors of the QCD phase diagram within $mu_B in (500, 900)$ MeV, and affect the position of the critical end point.
We elucidate how the color neutrality is harmed in the Polyakov Nambu-Jona Lasinio (PNJL) model at finite density within the adopted mean field approximation. Also we point out how usual assumption about the diagonal form of the Wilson loop may fail in the presence of the diquark condensate on several grounds.
We study how the charge neutrality affects the phase structure of three-flavor PNJL model. We point out that, within the conventional PNJL model at finite density the color neutrality is missing because the Wilson line serves as an external ``colored field coupled to dynamical quarks. In this paper we heuristically assume that the model may still be applicable. To get color neutrality one has then to allow non vanishing color chemical potentials. We study how the quark matter phase diagram in $(T,m_s^2/mu)$-plane is affected by imposing neutrality and by including the Polyakov loop dynamics. Although these two effects are correlated in a nonlinear way, the impact of the Polyakov loop turns out to be significant in the $T$ direction, while imposing neutrality brings a remarkable effect in the $m_s^2/mu$ direction. In particular, we find a novel unlocking transition, when the temperature is increased, even in the chiral SU(3) limit. We clarify how and why this is possible once the dynamics of the colored Polyakov loop is taken into account. Also we succeed in giving an analytic expression for $T_c$ for the transition from two-flavor pairing (2SC) to unpaired quark matter in the presence of the Polyakov loop.
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